The article presents the evolution of seismic monitoring of the territory of Moldova Republic. The more important stages of development of the National Network of Seismic Stations - from the early analog recordings to the digital recordings in real time - are presented. The recent Network modernization with digital equipment and the creation of the National Data Centre has offered he possibility for operational assessment of the seismic events and integration into the global seismic stations network. Also, the perspective of development of the Earthquake Warning System or Chişinău city, importance of the Data Centre in informing the society and education of the population about earthquakes are described.